如圖,△ABC中,D為BC的中點,G為AD的中點,過點G任作一直線MN分別交AB、AC于M、N兩點.若
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=x
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,
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=y(tǒng)
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,求
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的值.
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設(shè)
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=
a,
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=
b,則

=x
a,
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=y(tǒng)
b,
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=
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=
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(
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+
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)=
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(
a+
b).
∴
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=
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-
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=

(
a+
b)-x
a=
a+
b,
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=
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-

=y(tǒng)
b-x
a=-x
a+y
b.
∵
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與
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共線,∴存在實數(shù)λ,使

=λ

.
∴
a+
b=λ(-x
a+y
b)=-λx
a+λy
b.
∵
a與
b不共線,∴

消去λ,得

=4.
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